Question
6. Bo and Li are standing 325 m apart,watching a hot air balloon above hem. Bo measures the angle of elevation to the balloon to be 54 degrees measures the angles of elevation to the balloon to be 38 degrees.How is each person from the balloon , to the nearest metre. Find the height balloon, to the nearest metre.
Solution
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(86 Votes)
Jordan
Veteran · Tutor for 11 years
Answer
### Bo is approximately 201 meters from the balloon, Li is approximately 263 meters from the balloon, and the balloon is approximately 163 meters high.
Explanation
## Step 1: Visualizing the Problem### We have two observers, Bo and Li, a certain distance apart, looking at a hot air balloon. This forms a triangle. We know the distance between Bo and Li, and the angles of elevation from each of them to the balloon.## Step 2: Setting up the Triangle### Let B be Bo's position, L be Li's position, and H be the point on the ground directly below the balloon. Let the balloon's position be A. We have triangle BLH with BL = 325m. Let x be the distance BH. Then LH = 325 - x. Angle ABH = 54° and angle ALH = 38°. Let h be the height of the balloon, AH.## Step 3: Using Trigonometry### In triangle ABH,
. In triangle ALH,
.## Step 4: Solving for x### From the equations in Step 3, we have
and
. Therefore,
. This simplifies to
. So,
.## Step 5: Calculating x### Using a calculator,
and
. Therefore,
m.## Step 6: Calculating h### Now we can find h using
.
m.## Step 7: Calculating Distances to the Balloon### Distance from Bo to the balloon (AB) is
m.### Distance from Li to the balloon (AL) is
m.